SOLUTION: Help!? I am only in Grade 5 and I don't understand this! A box contains the letters M A S S A C H U S E T T S Without looking in the box how many letters do you need to pick fro

Question 837681: Help!? I am only in Grade 5 and I don't understand this!
A box contains the letters
M A S S A C H U S E T T S
Without looking in the box how many letters do you need to pick from the box to be certain you can make the word SAT?

Found 2 solutions by josmiceli, Theo:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Imagine you are doing what they ask. You
are reaching in the box and picking letters
one at a time.
What they are looking for is the "worst case"
which is the hardest way possible to get SAT.
So imagine this is the order in which you
pull out letters:
M
C
H
U
E
5 letters so far and no S,A, or T
--------------------
Now say, the nest letters you get are:
S
S
S
S
That helps, but you only have 1 letter to make SAT
You've got 9 letters so far
---------------------
The next letters you get are:
T
T
11 letters so far, but you're missing the A
---------------------
The only letters left in the box are A,A so
the next pick gives you SAT
---------------------
That makes 12 letters needed to be CERTAIN that you
have SAT because you know this the the worst
case that can happen

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the word is MASSACHUSETTS.
there are 4 letter S and 2 letter A and 2 letter T in the word.
you only need 1 or each to form the word SAT.
there are 13 letters total in the word MASSACHUSETTS.
you pick all 13 letters.
are you guaranteed that, out of the 13 letters that you picked, you can form the word SAT?
the answer is yes because you have all the letters.
in fact, you have 4 letter S and 2 letter A and 2 letter T.
you have more than enough to form the word SAT.

now let's say you pick 12 letters and leave 1.
are you guaranteed that, out of the 12 letters that you picked, you can form the word SAT?
the answer is yes again because, even if the letter that you didn't pick was the letter T, you still have enough to form the word SAT.
you would have picked 4 letter S and 2 letter A and 1 letter T.
that's still enough to form the word SAT out of the letters that you picked.

now let's say you pick 11 letters and leave 2.
are you guaranteed that, out of the 12 letters that you picked, you can form the word SAT?
the answer is no because, assuming the 2 letters that you didn't pick up were the letter T, then you would have picked up 4 letter S and 2 letter A but no letter T which is not enough to form the word SAT since SAT requires a T that you didn't pick up.

so, in order to be guaranteed (100% certain) that you can form the word SAT from the letters that you picked up, you have to pick 12 letters.

picking less than 12 letters will not guarantee that you can form the word SAT because the 2 letters that you didn't pick up could both be a T or both be an S which would not leave you with enough letters to form the word SAT.

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